Results 101 to 110 of about 175 (113)

Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the lebesgue space

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author shows that, for a subset \(X\) of \(L_1\) which is compact in measure, the continuity, demicontinuity, and weak sequential continuity of \(T: X\to X\) are equivalent. This makes it possible to enlarge the applicability of fixed point theorems involving weakly condensing operators.
Józef Banas
exaly   +3 more sources

Weakly demicompact linear operators and axiomatic measures of weak noncompactness

Mathematica Slovaca, 2019
Abstract In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O’REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover,
Bilel Krichen
exaly   +2 more sources

Measures of Weak Noncompactness and Fixed Points

2017
The interaction between measures of weak noncompactness and fixed point theory is really strong and fruitful. In particular, measures of weak noncompactness play a significant role in topological fixed point problems. The purpose of this chapter is to exhibit the importance of the use of measures of weak noncompactness in topological fixed point theory
Agnieszka Chlebowicz, Mohamed Aziz Taoudi, Taoudi Mohamed-Aziz   +2 more
exaly   +2 more sources

Measure of weak noncompactness, some new properties in Fredholm theory, characterization of the Schechter essential spectrum and application to transport operators

Ricerche Di Matematica, 2012
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Aref Jeribi, Maher Mnif, Jeribi Aref
exaly   +3 more sources

On some parameters related to weak noncompactness in L1(μ,E)

Quaestiones Mathematicae, 2009
A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU(A) of a bounded set A in the Bochner space L1(μ,E) and two parameters Π(A) and Λ1(A)
Diana Caponetti
exaly   +1 more source

Stability of relative essential spectra of the transport operator in $$L^1$$-space by means of measures of noncompactness and relative weak demicompactness

Monatshefte für Mathematik, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chelly, Slim, Jeribi, Aref, Krichen, Bilel   +2 more
openaire   +2 more sources

On measures of weak noncompactness

Publicationes Mathematicae Debrecen, 1994
A notion of measure of weak noncompactness is introduced which generalizes the De Blasi measure of weak noncompactness. Some properties of this generalized measure are proved. The existence of bounded weak solutions of certain differential equations is shown.
openaire   +1 more source

Convexification of super weakly compact sets and measure of super weak noncompactness

Proceedings of the American Mathematical Society, 2021
In the paper, we give a quantitative version of the positive answer to the open question about the convex hull of a super weakly compact set. Measure of super weak noncompactness σ
openaire   +2 more sources

Measures of weak noncompactness, nonlinear leray-schauder alternatives in banach algebras satisfying condition (p) and an application

Quaestiones Mathematicae, 2015
In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
Ali, Amro Alsheikh, Amar, Afif Ben
openaire   +2 more sources

Measures of weak noncompactness and fixed point theory in banach algebras satisfying condition (P)

2017
The aim of this paper is to prove some new fixed point theorems in a nonempty closed convex subset of a Banach algebra satisfying a sequential condition (P) in a weak topology setting.
Ben Amar, Afif, O’Regan, Donal
openaire   +1 more source